`BookProof.TensorCore.tmul_mem_corePow` {n : ℕ} {a : D₂} (ha : (a : Hs.carrier) ∈ D) {b : ((domSpace Hs D₂).pow n)} (hb : b ∈ corePow Hs D₂ D n) : a ⊗ₜ[ℂ] b ∈ corePow Hs D₂...

Proved

BookProof.TensorCore.tmul_mem_corePow

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.tmul_mem_corePow {n : ℕ} {a : D₂} (ha : (a : Hs.carrier) ∈ D) {b : ((domSpace Hs D₂).pow n)} (hb : b ∈ corePow Hs D₂ D n) : a ⊗ₜ[ℂ] b ∈ corePow Hs D₂ D (n + 1)

Formalization note: Lean 4 identifier BookProof.TensorCore.tmul_mem_corePow.

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.tmul_mem_corePow
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Mathlib
import Definitions.Def_ChapterTensorGraphCore
open BookProof.TensorCore



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore

noncomputable section

variable (Hs : IPSpace) (D₂ : Submodule ℂ Hs.carrier)
variable (A : D₂ →ₗ[ℂ] Hs.carrier)
variable (D : Submodule ℂ Hs.carrier)

Formal statement

theorem BookProof.TensorCore.tmul_mem_corePow {n : ℕ} {a : D₂} (ha : (a : Hs.carrier) ∈ D)
    {b : ((domSpace Hs D₂).pow n)} (hb : b ∈ corePow Hs D₂ D n) :
    a ⊗ₜ[ℂ] b ∈ corePow Hs D₂ D (n + 1) := by sorry

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